Hinton - The Fourth Dimension.pdf

80
THE FOURTH DIMENSION
Let us consider a sphere of our three-dimensional
z
F
D
Fig. 44.
Axis of x running towards
the observer.
matter having a definite
thickness. To represent
this thickness let us suppose
that from every point
of the sphere in fig. 44 rods
project both ways, in and
out, like D and F. We can
only see the external portion,
because the internal
parts are hidden by the
sphere.
In this sphere the axis
of x is supposed to come
towards the observer, the
axis of z to run up, the axis of y to go to the right.
Now take the section determined by the xy plane.
z
w
E
Fig. 45.
F
C
D
y
This will be a circle as
shown in fig. 45. If we
let drop the x axis, this
circle is all we have of
the sphere. Letting the
w axis now run in the
plane of the old x axis
we have the space yzw
and in this space all that
we have of the sphere is
the circle. Fig 45 then
represents all that there
is of the sphere in the
space of yzw. In this space it is evident that the rods
CD and EF can turn round the circumference as an axis.
If the matter of the spherical shell is sufficiently extensible
to allow the particles C and E to become as widely
separated as they would in the positions D and F, then
y